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I have taken my data and created a second degree polynomial for all continuous numeric terms. I have more of a theoretical question: is it valid to run a lasso regression on these polynomials? Or can lasso only be run on the base variables that are NOT polynomials.

For example, I worry that lasso doesn't consider the base effect, and may just select the second order one blindly.

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  • $\begingroup$ A polynomial term for a continuous predictor is just an interaction term with itself. Considerations about omitting a "main effect" while keeping an interaction in LASSO (what troubles you here) are covered on this page. It might be OK, depending on your purpose in modeling. Consider editing your question to say more about your study, as you might be able to accomplish what you want with other methods. It's hard to know what to suggest without more information about your data and the questions you are trying to answer. $\endgroup$
    – EdM
    Oct 27, 2023 at 19:05
  • $\begingroup$ That page answers my question -- thanks. I was wondering more in general rather that w.r.t. my specific dataset. And it sounds like the answer is "it depends, but it is not inherently wrong". I do wonder if orthogonal polynomials were considered when people gave their answers, however... $\endgroup$
    – Aegis
    Oct 27, 2023 at 19:54

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